I downloaded and mounted the iso to install the 64 bit wubi, but every time I run it it gets stuck on "Downloading ubuntu-12.04.2-wubi-amd64.tar.xz . I've seen other people with this problem who never seem to get it solved.

I'm running on a 64-bit Windows 7 Home Premium machine, my internet connection is fine, I'm just not sure what the problem is or how to fix it.

How long have you been waiting? It usually takes a long time.
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LinuxiosMar 20 '13 at 3:08

2

There is a bug in Wubi 12.04.2 that cannot use the ISO (you shouldn't mount it either but that won't help because of the bug). Therefore there is no point in downloading it. Wubi.exe must instead download the diskimage (500MB) so that will take some time. You can manually download it, but the it requires a --dimagepath= argument to find it as explained here
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bcbcMar 20 '13 at 3:17

It's not stuck, it downloads slow even in fast networks because Wubi can't download amd64.tar.xz very fast, actually, mine is even slow, but if you have an extreme network like 4mbps or higher, I think because I have 3mbps, I waited and when the 15 minutes is actually 10 minutes but I felt like it was 20 minutes waiting time. So if you don't understand how this works, use the CD Installation of Ubuntu to have no waiting time for this.

If it still doesn't download wubi-amd64.tar.xz, this might be a bug on the 12.04.02, and maybe try using the 12.04.01 version of download (using the CD, maybe), and never mount the ISO, or it might cause problems.